29 research outputs found
Deformations of symmetric CMC surfaces in the 3-sphere
In this paper we numerically construct CMC deformations of the Lawson minimal
surfaces using a spectral curve and a DPW approach to CMC surfaces
in spaceforms.Comment: 17 pages, 5 figure
Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms
We present a theorem on the unitarizability of loop group valued monodromy
representations and apply this to show the existence of new families of
constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in
the simply-connected 3-dimensional space forms , \bbS^3 and \bbH^3.
Additionally, we compute the extended frame for any associated family of
Delaunay surfaces.Comment: 18 pages, revised versio
Bifurcating extremal domains for the first eigenvalue of the Laplacian
We prove the existence of a smooth family of non-compact domains bifurcating from the straight cylinder for
which the first eigenfunction of the Laplacian with 0 Dirichlet boundary
condition also has constant Neumann data at the boundary. The domains
are rotationally symmetric and periodic with respect to the R-axis of the
cylinder; they are of the form where and T_0 is a
positive real number depending on n. For these domains provide a
smooth family of counter-examples to a conjecture of Berestycki, Caffarelli and
Nirenberg. We also give rather precise upper and lower bounds for the
bifurcation period T_0. This work improves a recent result of the second
author.Comment: 28 pages, 3 figure